Equilibrium payoffs in repeated two-player zero-sum games of finite automata

Abstract

Repeated two-player zero-sum games of finite automata are studied. The players are charged a penalty proportional to the size of their automata to limit the complexity of strategies they can use. The notion of bounded computational capacity equilibrium payoff is thus transferred to the case of zero-sum games. It is proved that the set of bounded computational capacity equilibrium payoffs contains exactly one value, namely the value of the one-shot game, or, equivalently, that the value of the game with penalty approaches the value of the one-shot game as the penalty goes to zero. An estimate of the rate of convergence is also provided.